Regular Expression Matching and Operational Semantics

Many programming languages and tools, ranging from grep to the Java String library, contain regular expression matchers. Rather than first translating a regular expression into a deterministic finite automaton, such implementations typically match the regular expression on the fly. Thus they can be seen as virtual machines interpreting the regular expression much as if it were a program with some non-deterministic constructs such as the Kleene star. We formalize this implementation technique for regular expression matching using operational semantics. Specifically, we derive a series of abstract machines, moving from the abstract definition of matching to increasingly realistic machines. First a continuation is added to the operational semantics to describe what remains to be matched after the current expression. Next, we represent the expression as a data structure using pointers, which enables redundant searches to be eliminated via testing for pointer equality. From there, we arrive both at Thompson's lockstep construction and a machine that performs some operations in parallel, suitable for implementation on a large number of cores, such as a GPU. We formalize the parallel machine using process algebra and report some preliminary experiments with an implementation on a graphics processor using CUDA.Comment: In Proceedings SOS 2011, arXiv:1108.279

A Bigraph Relational Model

In this paper, we present a model based on relations for bigraphical reactive systems [Milner09]. Its defining characteristics are that validity and reaction relations are captured as traces in a multi-set rewriting system. The relational model is derived from Milner's graphical definition and directly amenable to implementation.Comment: In Proceedings LFMTP 2011, arXiv:1110.668

Pervasive Process Calculus

AbstractProcess calculi with various signatures and reaction rules may provide a theoretical basis for pervasive computing

Fully abstract models of typed λ-calculi

AbstractA semantic interpretation A for a programming language L is fully abstract if, whenever A〚C[M]〛⊑A〚C[N]〛 for two program phrases M,N and for all program contexts C[ ], it follows that A〚M〛⊑A〚N〛. A model M for the language is fully abstract if the natural interpretation A of L in M is fully abstract.We show that under certain conditions there exists, for an extended typed λ-calculus, a unique fully abstract model